Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D281 |
| commutator, socle, cosocle | C22×C281 | C24 |
| Fitting | #120×C281 | C2 |
| hypercenter | #120 | D281 |
| hypocenter | C281 | #560 |
| LCS | G ▷ C22×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22582875 | C2 | semidirect |
| 2. #22582872 | C2 | semidirect |
| 3. #22582861 | C2 | semidirect |
| 4. #22582860 | C2 | semidirect |
| 5. #22582852 | C2 | semidirect |
| 6. #22582851 | C2 | semidirect |
| 7. #22582850 | C2 | semidirect |
| 8. #22582848 | C2 | semidirect |
| 9. #120×C281 | C2 | semidirect |
| 10. C2×D1124 | C22 | semidirect |
| 14. C2×C22⋊D281 | C22 | semidirect |
| 15. C22×Dic281 | C22 | semidirect |
| 16. C2×C4×D281 | C22 | semidirect |
| 17. C4⋊Dic281 | C22 | semidirect |
| 18. #17985117 | C22 | semidirect |
| 19. #17985117 | C22 | semidirect |
| 23. C22⋊Dic281 | C22 | semidirect |
| 24. #17985115 | C22 | semidirect |
| 25. C4×Dic281 | C22 | semidirect |
| 74. C281 | #560 | semidirect |
| 84. #120 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582875 | 2 |
| #22582872 | 2 |
| #22582861 | 2 |
| #22582860 | 2 |
| #22582852 | 2 |
| #22582851 | 2 |
| #22582850 | 2 |
| #22582848 | 2 |
| #120×C281 | 2 |
| #560 | 281 |